Answer:
The t value for 99% CI for 21 df is 2.831.
The critical value that should be used in constructing the confidence interval is (64.593, 86.407).
Step-by-step explanation:
Now the sample size is less than 30 and also population standard deviation is not known.
Then we will use t distribution to find CI
t value for 99% CI for 21 df is TINV(0.01,21)=2.831
The margin of error is [tex]E=t\times\frac{s}{\sqrt{n}}\\\\=2.831\times\frac{18.07}{\sqrt{22}}\\\\=10.907[/tex]
Hence CI is[tex]CI=\overline{x} \pm E\\\\ =75.50 \pm 10.907\\\\=(64.593,86.407 )[/tex]
The survey included a random sample of 640 western residents and 540 northeastern residents. 39% of the western residents and 51% of the northeastern residents reported that they were completely satisfied with their local telephone service. Find the 99% confidence interval for the difference in two proportions
Answer:
The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Western residents:
39% out of 640, so:
[tex]p_1 = 0.39[/tex]
[tex]s_1 = \sqrt{\frac{0.39*0.61}{640}} = 0.0193[/tex]
Eastern residents:
51% out of 540, so:
[tex]p_2 = 0.51[/tex]
[tex]s_2 = \sqrt{\frac{0.51*0.49}{540}} = 0.0215[/tex]
Distribution of the difference:
[tex]p = p_2 - p_1 = 0.51 - 0.39 = 0.12[/tex]
[tex]s = \sqrt{s_2^2+s_1^2} = \sqrt{0.0215^2+0.0193^2} = 0.0289[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.12 - 2.575*0.0289 = 0.0456[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.12 + 2.575*0.0289 = 0.1944[/tex]
The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).
Given: Measure of arc AB = measure of arc BC,
Measure of angle x = 60°, measure of angle y = 15°
Find: Measure of arc AC
9514 1404 393
Answer:
100°
Step-by-step explanation:
The relevant relation for angle x is ...
x = (AB +DE)/2
and for angle y, it is ...
y =(AC -DE)/2
Using the second relation to write an expression for DE, we have ...
DE = AC -2y
In the first equation, this lets us write ...
x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2
2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2
(2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3
AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values
AC = 100°
Define business.Write the type of business
Answer:
A company or an entrepreneurial entity engaged in commercial, industrial, or professional activity is referred to as a business. A limited liability company (LLC), a sole proprietorship, a corporation, and a partnership are examples of different types of businesses.
Find the least whole number N so that 123+N is a perfect square.
21
12^2 = 144
144 - 123 = 21
11^2 = 121
12^2 = 144
Between these
Answered by Gauthmath must click thanks and mark brainliest
Solve.
x^2 - 9x + 3 = 0
x= or x=
Answer:
Step-by-step explanation:
x^2 - 9x + 3 = 0 is a quadratic whose coefficients are a = 1, b = -9 and c = 3.
Use the quadratic formula to solve it.
The discriminant, b^2 - 4ac, is 81 - 4(1)(3), or 81 - 12, or 69.
The roots are:
-b ± √(discriminant)
x = -------------------------------
2a
And these roots in this particular problem are:
-(-9) ± √69 9 ± √69
= ------------------------------- = ----------------
2(1) 2
Mr.Peter earned $25 per week how much does he earned in a year
Answer: Approximately $1,300
Step-by-step explanation:
There is around 52 weeks in a normal year.
$25 · 52 = $1300
Answer:
1300
Step-by-step explanation:
There are 52 weeks in a year
52 * 25 = 1300
Which statement is true about the ratios of squares to
cicles in the tables? PLS HURRY!!!!
Answer:
show us a screenshot or image
or type it out, copy paste
Step-by-step explanation:
Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please.
The number of cubic feet of water in a curved container can be approximated by V=0.95h^2.9 find the amount of water in the container when h=8 feet round to the nearest tenth
Answer choices:
A. 0.9
B. 358.4
C. 395.1
D. 314.9
Answer:
C. 395.1
Step-by-step explanation:
Substitute the value for x:
[tex]V=0.95(8)^{2.9}\\V=395.1[/tex]
Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y = 10,000 – 250x and the value of the car after x months is represented by y = 8,000 – 50x. Which statement describes when Melinda’s loan will be equal to the value of the car?
After 10 months, the loan and value of the car will both be equal to $7,500.
After 12 months, the loan and value of the car will both be equal to $7,000.
After 14 months, the loan and value of the car will both be equal to $6,500.
After 16 months, the loan and value of the car will both be equal to $6,000.
Answer:
After 10 months, the loan and value of the car will both be equal to $7,500.
Step-by-step explanation:
Value of the loan after x months:
[tex]y_l = 10000 - 250x[/tex]
Value of the car after x months:
[tex]y_c = 8000 - 50x[/tex]
Which statement describes when Melinda’s loan will be equal to the value of the car?
They are equal when:
[tex]y_l = y_c[/tex]
So
[tex]10000 - 250x = 8000 - 50x[/tex]
[tex]200x = 2000[/tex]
[tex]x = \frac{2000}{200}[/tex]
[tex]x = 10[/tex]
Equal after 10 months:
Value of [tex]y(10) = 8000 - 50(10) = 7500[/tex]
Thus, the correct option is:
After 10 months, the loan and value of the car will both be equal to $7,500.
please help, will give brainliest!!!!
Answer:
3
Step-by-step explanation:
3 - 3/x
----------------
1 - 1/x
Multiply the top and bottom by x
x(3 - 3/x)
----------------
x(1 - 1/x)
3x -3
------------
x-1
Factor the numerator
3(x-1)
-------
x-1
Cancel like terms
3
-----
1
3
Which expression is equivalent to 6x3 + 3y2 – 5x3 + 2y2?
Answer:
The answer is c because6X^3 minus 5X^3 is just X^3 and 3Y^2 plus 2Y^2 is 5Y^2.
si 40/a = 35/7 entonces cual es el valor de a
Respuesta:
a = 8
Explicación paso a paso:
Para obtener el valor de a en la ecuación:
40 / a = 35/7
Cruzamos multiplicamos:
40 / a = 35/7
40 * 7 = 35 * a
280 = 35a
Dividir ambos lados por 35
280/35 = 35a / 35
8 = a
a = 8
8 ^ 3 −9⋅2÷3 can someone please help me quickly
Answer:
506
Step-by-step explanation:
8³-9×2÷3
= 512 - 9 × 2 ÷3
= 512 - 9 × ⅔
= 512 - 3 × 2
= 512 - 6
= 506
PEDMAS rule
P: Parentheses
E: Exponent
D: Division
M: Multiplication
A: Addition
S: Substraction
Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
For octagon =1080.......
Explanation:
180(8-2)
180×6
1080°
Need to know Anwser yes or no
Answer:
Reflective symmetry over the line y = 4 is No
Reflective symmetry over the line y = 1/7x + 3 is Yes
I NEED THE ANSWER SOON PLEASE!!?!?! hopefully someone sees this
Answer:
1 and 1/25
Step-by-step explanation:
PLSSS HELP IM STRUGGLING SO HARD !!! ———————
Answer:
C)
Step-by-step explanation:
Just see the length of the R line, A and B are almost the same large when you add them.
Enter the ratio as a fraction in lowest terms
6 minutes to 30 minutes.
6 minutes / 30 minutes
Divide the top and bottom by 6.
1 minute / 5 minutes
Fraction in lowest terms: 1/5
Hope this helps!
If 15% of the customer's total is $22.05, then the customer's total is
Answer:
$147
Step-by-step explanation:
0.15x = $22.05
Divide both sides by 15
22.05/0.15 = $147
210
To rationalize the denominator of
3.11,You should multiply the expression by which fraction?
11
2- V10
2- 10
3- V11
3- V11
We should multiply the expression by √11/ √11 fraction.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
To rationalize this, we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 2-√10 and its conjugate is; (2+√10).
(2√10)/(3√11) = (2√10)/(3√11)
= ((2√10)√11/(3√11) √11
= (2√110)/33
This is the rationalized expression.
Learn more about multiplications;
brainly.com/question/14059007
#SPJ7
Your car can go 2/7 of the way on 3/8 of a tank of gas how far can you go on the remaining gas?
A proportion that can be used is a/b=c/d
Answer:
10/21 of the distance
Step-by-step explanation:
2/7 distance
------------------
3/8 tank
The rest of the tank is 8/8 - 3/8 = 5/8
2/7 distance x
------------------ = ----------------------
3/8 tank 5/8 tank
Using cross products
2/7 * 5/8 = 3/8x
10/56 = 3/8x
Multiply each side by 8/3
10/56 * 8/3 = 3/8x * 8/3
10/3 * 8/56=x
10/3 * 1/7 =x
10/21 =x
10/21 of the distance
in the box of Stones ,the ratio of red marbles is 2:5. the ratio of green stones to the total stones is 3:10 .if the stones that are neither red nor green are blue ,how many blue are in the box.if there are 40 marbles in the box?.
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to thegiven statistics and confidence level. Round the margin of error to four decimal places.1)99% confidence; n
Answer:
[tex]E = 0.0158[/tex]
Step-by-step explanation:
Given
[tex]n = 5900[/tex]
[tex]x = 1770[/tex]
[tex]CI = 99\%[/tex]
Required
The margin of error (E)
First, calculate proportion p
[tex]p = x/n[/tex]
[tex]p = 1770/5900[/tex]
[tex]p = 0.3[/tex]
Given that:
[tex]CI = 99\%[/tex]
Calculate the alpha leve;
[tex]\alpha = 1 - CI[/tex]
[tex]\alpha = 1- 0.99[/tex]
[tex]\alpha= 0.01[/tex]
Divide by 2
[tex]\alpha/2= 0.01/2[/tex]
Subtract from 1
[tex]1 - \alpha/2= 1 - 0.01/2[/tex]
[tex]1 - \alpha/2= 0.995[/tex]
The corresponding z value is:
[tex]z =2.576[/tex]
So, the margin of error is:
[tex]E = z * \sqrt{p * (1 - p)/n}[/tex]
So, we have:
[tex]E = 2.576 * \sqrt{0.3 * (1 - 0.3)/5600}[/tex]
Using a calculator, we have:
[tex]E = 0.01577471394[/tex]
Approximate
[tex]E = 0.0158[/tex]
Can someone help please
( x - 2 )( x - 8 )( x + 5 ) =
( x^2 - 10x + 16 )( x + 5 ) =
x^3 - 10x^2 + 16x + 5x^2 - 50x + 80 =
x^3 + ( - 10 + 5 )x^2 + ( 16 - 50)x + 80 =
x^3 - 5x^2 - 34x + 80
If x+y=
= 12 and x = 2y, then x =
O
2
06
08
10
Answer:
2y + y = 12
3y = 12
y = 4
now , x = 2y
x = 2 ( 4 )
x = 8
hope that helps ✌
what is the length of GN, given that figure LMNO is a square PLZ HELP!!!!!
Answer:
A. 4
Step-by-step explanation:
The diagonals are also congruent to each other. Diagonals of a square bisect each other. This implies that:
MO bisects LN, thereby dividing LN into two equal segments, LG and GN.
Thus, LG = GN.
Since the length of LG = 4, therefore:
GN = 4
find the perimeter of 6 CM 6 CM 6 CM 6 CM
Answer:
P = 24
Step-by-step explanation:
Since all the sides are the same length, the shape is a square.
Multiply all sides by 6.
6 cm x 4 sides = 24
Form a union for the following sets.
M = {1, 2, 4, 8)
N = (2,5,8)
Answer:
Step-by-step explanation:
When you are asked to find the union of sets you find numbers that are present in both sets.
So a number that appears in both the sets of M and N are 2 and 8.
So M U N = { 2,8} where U is the symbol for union.
Can someone help me out
Answer:
236m^2
Step-by-step explanation:
8x5=40x2=80
6x5=30x2=60
6x8=48x2=96
80+60+96=236
